Perceiving
Egospeed in the
Fog: Effects of
Global Optical
Flow Rate and
Contrast
Master’s Thesis Proposal
Andy Schaudt
University of Idaho
April 30th, 2004
Overview
•
•
•
•
•
•
•
Introduce egospeed in fog
Optical factors of influence on egospeed
Contrast
Global Optical Flow Rate
Failure to investigate
Purpose of proposed research
Proposed experimental method
Egospeed & Fog
• Fog
– 1,387 highway deaths 2001 alone (L.A. Times, 2002)
– Many due to misjudgment of speed
Egospeed & Fog
• Egospeed – Perception of the speed of selfmotion
• Optical factors that influence perceived
egospeed:
–
–
–
–
Global Optical Flow Rate (GOFR)
Edge Rate (ER)
Motion Parallax
Contrast
Fog
• Fog
– Water Vapor
– Reflects and scatters light
Fog
• Dispersion of light reduces the
transparency of the air reducing contrast
and limiting visibility-distance
• Visibility-distance – distance from the eye
to the set of visible objects
Contrast
• Gjon (1935) stated fog reduces contrast
and reduces a signal’s beam through
diffusion
• Brooks (2001) reduction in contrast
reduces perceived speed
• Thompson Effect – reduction in contrast
also reduces perceived speed
Global Optical Flow Rate
• Dyre, Ballard, and McDevitt (2004) found that
GOFR is the primary basis for egospeed
estimates
• GOFR – rate of egospeed scaled in eye-heights
relative to a planar surface
V
GOFR p 
D
Example
9000m
GOFR = 0.028 eye-heights s-1
GOFR = 1.25 eye-heights s-1
• GOFR may be higher while walking and much lower
during flight at high speeds and altitudes
• Leads to the misperception of slower travel while flying
Global Optical Flow Rate
• A more general distance metric for nonplanar and planar environments, Dyre, Ballard,
and McDevitt (2004)
• GOFR relative to any arbitrary
environment can be defined as:
GOFR 
V
 V
R
1
N

i 1

X  Yi  Z
2
i
2
N
2
i
NV
N

i 1
X i2  Yi 2  Z i2
Effect of Fog
• Average visibility distance – average
distance from the eye to the set of visible
objects
• Contrast gradient – contrast of an object is
reduced as a function of depth or distance
• At some distance, contrast is reduced to
zero obscuring any objects that lie beyond
this distance
Fog’s Effects
• 3 different scenarios of fog
No Contrast
Global Contrast
Linear Fog
Contrast Gradient
Contrast Gradient - Fog
Contrast Gradient - Fog
Contradicting Findings
• Contrast and GOFR influence egospeed
• Fog affects both optical parameters
Contrast
Reduction in Egospeed
GOFR
Increase in Egospeed
Previous Study
• Snowden, Stimpson, & Ruddle, (1998) –
Reduction of global contrast increased
perceived speed
• Conclusion – contrast reduction due to fog
causes drivers to perceive egospeed as
slower and increase speed to compensate
• Failure to investigate GOFR in regards to
object distance
Fog’s Effects
• Fog reduces maximum visibility distance in
the environment
• Constrains the sampling of optical flow to
objects closest to the observer, increasing
GOFR
• Currently no research has investigated the
effect of fog on perception and control of
egospeed that includes this contrast
gradient
Purpose of Proposed Research
• Purpose: To examine the effect of GOFR
and contrast on the perception of
egospeed in a foggy environment
• Contrast will be manipulated to the
environment in the following:
– Introduce levels of a linear contrast gradient
– Introduce levels of global contrast
Hypothesis 1
• Hypothesis 1 – Fog can affect visually
perceived speed due to reduced visibility
distance, which changes the sampling of
optical flow to emphasize nearby objects
– This will create an increase in both GOFR and
perceived speed, and a driver may decrease
speed to compensate
Hypothesis 2
• Hypothesis 2 – Fog can affect visually
perceived speed by reducing overall
contrast
– This will create a decrease in perceived
speed and a driver may increase speed to
compensate
Contradicting Predictions
• These contradicting predictions suggest
that the relationship between fog and
perceived speed is complex
• Both overall contrast and visibility distance
need to be taken into account
Proposed Experimental Methods
• Propose 2 experiments
– 1) Two-alternative sequential presentation
method to investigate the effects of a contrast
gradient on perceived egospeed while holding
overall contrast constant
– 2) Adjustment of speed method to examine
whether the effects of overall contrast and
visibility distance on perceived speed
generalize to control of speed
Both Experiments
• Participants
– Eight undergraduates students for each
experiment
– 20/30 or better corrected Snellen acuity
– Naïve to purpose
Experiment 1: Stimuli & Apparatus
• Simulate driving over a flat textured
surface
• Presented on one 1.69m diagonal rear
projection monitor
• Fog will be presented as levels of a linear
contrast gradient (linear contrast)
Experiment 1: Stimuli & Apparatus
• Linear fog parameter equation used by OpenGL:
f z, end  
end  z 
end  start 
Parameter
Description
z
end
Depth
Defines the fog
start
f
Always equal to zero
1 – fog-density
Experiment 1: Stimuli & Apparatus
• f = 1 - fog-density
• It is always at its maximum value when:
z = start (a value of 1)
• It decreases linearly to completely opaque
(no contrast) when:
z = end (a value of 0)
Experiment 1: Stimuli & Apparatus
• The manipulation of linear fog will also
affect global contrast
• Necessary to maintain a constant global
contrast across contrast gradients
• How?
• Compensating for the covariance between
the contrast gradient and overall contrast
with the use of a translucent object similar
to a lens from a pair of sunglasses
Translucent Object
Experiment 1: Stimuli & Apparatus
end 2
1 end1 , end 2 ,  2   1 
 1   2 
end1
• Contains 2 important parameters
Parameter
Description
X2
Standard term
X1
Comparison term
Determines translucency

Experiment 1: Stimuli & Apparatus
• For example, if we enter the following values for
these parameters:
2 = .85
end2 = 125
• we can enter in values for end1 and find the
overall contrast level necessary
2
.85
.85
.85
.85
end2
125
125
125
125
end1
25
50
75
100
1
.25
.625
.75
.813
Experiment 1: Design
(Two-Alternative)
• A 2 x 5 x 5 within-subjects factorial design
will be used
• Independent Variables:
– Temporal Position of the standard stimulus
(first or second)
– Linear Contrast
– Observer Velocity
• Dependent Variable:
– Proportion of faster judgments for the
comparison stimulus
Experiment 1: Procedure
• Experiment will span 2 one-hour and
fifteen minute sessions
– Each session contains 500 trials
– 50 unique displays- 20 blocks
– Each trial will last approximately 7 seconds
– Each trial will present two displays, standard
and comparison
• Observers indicate
– Which display in each set resulted in a faster
perception of egospeed
Experiment 2: Stimuli & Apparatus
• Apparatus and general format of the
displays will be identical to Experiment 1
Experiment 2: Design
(Adjustment)
• A 3 x 3 x 3 within-subjects factorial design
will be used
• Independent Variables:
– Linear Contrast
– Overall Contrast
– Observer Velocity
• Dependent Variable:
– Adjusted speeds
Experiment 2: Procedure
• Experiment will span 2 one-hour and
fifteen minute sessions
– Each session contains 500 trials
– 50 unique displays- 20 blocks
– Each trial will last approximately 7 seconds
– Each trial will present two displays, standard
and comparison
• Observers indicate
– Which display in each set resulted in a faster
perception of egospeed
References
Blakemore, M.R., & Snowden, R.J., (1999). The effect of contrast upon perceived speed:
a general phenomenon? Perception, 28, 33-48.
Blakemore, M.R., & Snowden, R.J., (2000). Textured backgrounds alter perceived
speed. Vision Research, 40, 629-638
Brooks, K. (2001). Stereomotion speed perception is contrast dependent. Perception,
30, 725-731.
Dyre, B.P, Ballard, T.G., & McDevitt, J.R., (2004). Perception of egospeed: Effect of flow
rate on element density. Manuscript in preparation, University of Idaho.
Dyre, B.P., Kludt, K., & Schaudt, W.A., (2004). Onset of vection in simulated
environments. Unpublished raw data, University of Idaho..
Gibson, J.J. (1950). The perception of the visual world, Boston: Houghton Mifflin.
Gjon, M. (1935). Visibility of signals through fog. Journal of the Optical Society of
America, 25, 237-240.
McDevitt, J.R., (2001). Quantifying the biasing effect of motion parallax on speed
perception (Masters Thesis, University of Idaho).
References Continued..
Owen, D.H., Wolpert, L., & Warren, R. (1984). Effects of optical flow acceleration, edge
acceleration, and viewing time on the perception of egospeed acceleration. In d.H.
owen (Ed.) Optical flow and texture variables useful in detecting decelerating and
accelerating self-motion. (Interim technical report for Contract No. F33615-83-K0038, Task 2313-T3, pp. 79-133). Columbus: Ohio State University, Department of
Psychology, Aviation Psychology Laboratory.
Snowden, R.J., Stimpson, N., & Ruddle, R.A. (1998). Speed perception fogs up as
visibility drops. Nature, 392(6675), 450.
Thompson, P. (1982). Perceived rate of movement depends on contrast. Vision
Research, 22, 377-380.
Vartabedian, R. (2002). Clear need for response to fatal fog: Sensor systems could ease
the toll of horrific crashes amid road-obscuring weather conditions on highways in
California and elsewhere. L.A. Times, October 23 2002.
Warren, R. (1982). Optical transformation during movements: review of the optical
concomitants of egomotion. (AFOSR Grant Proposal number 81-0108). Columbus:
Ohio State University, Department of Psychology, Aviation psychology Laboratory.